Orthographic

The "view from space" projection: An azimuthal, perspective projection that is neither conformal nor equal area. Range is no more than one hemisphere at a time. This is the default Manifold projection for new drawings, images and labels components.

Scale

True at the center and along any circle having its center at the projection center but only in the direction of the circumference of the circle. Scale decreases with distance from the center.

Distortion

Only the center is free from distortion, which increases rapidly away from the center. Distortion is extreme near the edge of the hemisphere.

Usage

Pictorial views of the Earth, resembling those seen from space. This is a perspective projection of the globe onto a tangent plane from an infinite distance (i.e., orthogonally); thus, the map has the look of a globe. The Orthographic projection is used by default within Manifold for images and drawings that are not otherwise georegistered.

Limitations

Use only for a single hemisphere. Defined only for a sphere, specifically a sphere that utilizes the same major axis as the WGS84 datum, 6378137. Note that although WGS84 appears as a datum for Orthographic projection, the flattening of the WGS84 ellipsoid is ignored and only the major axis is used to define the sphere. Note that this is different than the explicitly enumerated Sphere datum, which utilizes a major axis of 6370997. Use the Stereographic projection instead of Orthographic if non-spherical datums are to be utilized.

Origin

Apparently developed by Egyptians and Greeks by the 2nd Century BC

Options

Specify the center of the projection by setting latitude origin and longitude origin. Specifying a non-Equatorial or non-polar origin causes an oblique projection. The Clip coordinates check box clips invisible parts of objects, such as countries located on the other side of the Earth from the point of view of the projection. Note that Clip coordinates is a destructive change: parts of objects extending beyond the projection horizon will be permanently trimmed.

The Southern Hemisphere view above is created using a latitude origin of -90 and a longitude origin of 0.

The Eastern Hemisphere view above is created using a latitude origin of 0 and a longitude origin of 90.

The Western Hemisphere view above is created using a latitude origin of 0 and a longitude origin of -90.

If more than one hemisphere is displayed, countries will be "wrapped" from the invisible side of the world and displayed anyway in mirror image.

Above is an Orthographic projection centered on latitude 68 North longitude -70. The original map included areas and a graticule for just the Northern Hemisphere. If zoomed far into the latitude and longitude origin we would see essentially zero distortion.

Using Clip Coordinates

The Clip coordinates checkbox in the Edit - Change Projection dialog tells Manifold to cut objects so that they do not "wrap" around the Orthographic coordinate system.

If we import the World_eg.mfd sample drawing and use Edit - Change Projection to re-project it into Orthographic centered on the default 0, 0 origin we will see that some areas, such as Australia and New Zealand are "wrapped" around the edge of the Orthographic system. This effect arises because the Orthographic projection is not intended to deal with more than one hemisphere's worth of data at a time.

To avoid this effect we have two choices:

·Edit the drawing in advance so that only areas in the hemisphere of interest exist. This is the method used to create the screenshots in the previous section of this topic.

·Check the Clip coordinates box and let Manifold "trim" objects to only those parts that are visible in the centered hemisphere. This works well in many situations but can be very slow to compute with large drawings since it is an extremely computationally expensive process (as will be seen from the operations reported in the progress dialogs it shows).

The illustration above shows the World_eg sample drawing after projection to Orthographic using Clip Coordinates. Note there is no overlap.

The Clip coordinates box is a convenience, not an exact cartographic instrument. It works by clipping objects using a clipping rectangle. If after using Clip coordinates in an Orthographic projection we re-project the World_eg drawing back into Latitude / Longitude we will see the areas have been clipped to fit inside a bounding box.

Using straight lines to clip objects at the Orthographic horizon is an imperfect approximation (it leads to a "lumpy" horizon sometimes at the edge of the Earth), but it is reasonably fast to compute.

Technical Note: Why is Clip Coordinates so Slow?

Users will soon learn that checking the Clip coordinates box changes the time required for a re-projection from nearly instantaneous to usually taking minutes or even hours although sometimes even with the Clip coordinates box checked the re-projection is still fast . Why is that?

Before Manifold System release 7.00 the Clip coordinates algorithms were relatively imprecise, trading accuracy away in order to gain speed. A side effect of that reduced accuracy was that in certain cases of very large data the error conditions accumulating from reduced accuracy would cause data to grow without end and result in a "no memory" error and a failed re-projection.

From release 7.00 the new Clip coordinates algorithms are much more accurate, using precision over 100 times greater than previously. In addition, the algorithms have been adjusted so that no matter how large the data set involved will Manifold run out of memory. The price of these changes for greatly improved accuracy and ability to handle very large data sets is that performance in all cases is really miserable. It is expected that future releases will introduce algorithmic improvements that will deliver performance gains.

In the meantime, users have two strategies to increase the performance when using the Clip coordinates box:

·Plan your work to schedule any re-projections requiring Clip coordinates for the end of your work day, so that the re-projection can be set cooking while you are away from the project and won't notice how long it takes. Plan big re-projections requiring Clip coordinates for the end of the day Friday when Manifold will have the entire weekend to crank away.

·Do re-projections only where the target center latitude is zero. A side effect of the algorithms used is that when the target center latitude is zero, the clipping areas used internally within the algorithms become much simpler and easier to compute and so the process goes much faster. As a result, if re-projecting to Orthographic where the target center latitude is zero, even with Clip coordinates checked the re-projection will still go reasonably fast.

Notes on Default Use of Orthographic Projection

Manifold uses Orthographic projection as a default projection when nothing is known about the geographic context of a component.

Geographic components imported into Manifold from geographically aware formats will automatically use whatever geographic context or projection is defined in the source file(s). Components (such as images and CAD drawings) imported from non-geographic formats will be imported as if they were in a meter-based Orthographic projection. Such components may acquire a geographic context at some point by georegistration but initially they are usually created in meter-based or pixel-based coordinate systems.

It makes sense to consider such components as being in Orthographic projection. Considering the small size of CAD drawings or images relative to the size of an entire Earth hemisphere, there is an essentially perfect correlation between the flat, Euclidean coordinates of the drawing or image space and the effectively flat, Euclidean coordinates of the very central portion of an Orthographic projection.

This convention of considering all abstract coordinate CAD drawings and pixel coordinate images to be emplaced within an Orthographic projection provides three main benefits:

·First, it allows standard dialogs for both geographic and non-geographic components because all components within Manifold are treated as geographic components.

·Second, it provides a simple way of dealing with geographic components imported from formats that do not store projection information: one imports the projection in a default way and then changes the component's projection properties to the required values.

·Third, many images used in GIS work are overhead images that may be assumed to be in Orthographic projection as a practical approximation for most purposes. This makes it relatively easy to georegister such images in a simple way.